Chapter 2

Experimental Techniques

The EPR instrumentation, crbstal growth and crystal structure of the

host lattices etc arc discussed bnetly in thls chapter. A brief account of the

evaluation of'the pnncipal \.aiues o f g and hrpet-tine tensors from EPR spectra

and the procedure for the evalua[ion t)f the direction cosines o f the metal ion

\\lien 11 cntcrs thc luttice suh~~ttuttoiiall! is also discussed. In addition, the

procedure fbr the estimation of spin-lattice relaxation times from variable

temperature EPR spectra. when the paramagnetic ions are incorporated in

paramagncttc lattices, is also discushcd A brief discussion about the EPR-

VMR and SimFonia computer programs, w hich are used in obtaining the spin-

l l a ~ n t l ~ o n t ~ n paranlctcrr ;inti ~ i i n u l ~ r i o n 01' the road maps and the powder

hpec1r.i. I \ ~ l a o presented

t.PK spectra of the pdr~rnq i i c t i c ion. doped In both diamagnetic and

paraindgicttc host l a t t ~ c s ~ arc dealt in this thesis. The paramagnetic ions

choacn 3:. [he host latrtce dre the onc, iihich are EPR silent at room

tempcr.triisc. When the tcrnperatusc I \ lo\\ cred, the paramagnetic ion of the

host I;ltfi~.e becomes EPR a d t i e and leads ti1 the broaden~ng of the hypertine

lines froill uhich the spin-lattice re1.1xati~in times betaeen the host m d the

ilill?ur~l) I> c~~lculatcd

EI'R spectra arc not usuall) recorded in pure paramagetic samples

except \+hen coopcrutii e phcnumcii~ Arc the main target a!' lnbestlgation. In

nlagnctically concentrated saruplcs, tllc. pdramagnetic centers are too close and

the spectrum is strongly affected by dipolar interactions as well as spin

exchange between the nelphhorinp centcrs. Hence. In order to derive

~ntbrmatlon contined to individual Ipuramabnetlc entitics, they need to be

separated, I.e., maget ical lq d~luted In solutions, this condition is readily

achlc\ cd at reasonably low conccntratlons. in solids, there are two common

methods.

One of tho method5 l h to dope the pa ramage t l c lmpurity in a

diomaynctic latticc or paramagnetic latt~ce, which IS EPR inactive at room

temperatures. I t ' the dopant concentrdtlon 15 sufficiently low (of the order o f 1

lnol ",, iri lcaa). thc stat1511c;li d~atrihuuon ot'the dopant centers is low enough

to a c h ~ c \ e the required bepardtlon, I h ~ \ iedds to well-resolved EPR spectra,

t r r r Iron: dipolar and exclidigt. ~ ' i t ' ~ , i t b and the treatment of the system as

~ndepcndenl centers 1s f a d ) ~ ~ s c p t a b l e .

Sucli doplng l a qultr ci~mrnilii ui th t rasi t ion metal complexes. In

thebe caaca, the dopant suhstancc necd not necessarily have the same crystal

structure JS the host l a t t~c r . Expsnnients show that the environment of the

host I.\ ~n \a r i ab ly forced <In the dopimt. thus m k i n g it possible to stud)

dopart ct~lnplex under sltuationa thdr do nor e.tist In 11s pure f o r m

l'hc other ~nethoti I > ti) p ! , ~ d u ~ e the paramagnetic centers in u

d i s i n ~ g ~ i c t ~ c lat t~cc. 'Thc IiliIat con111it111 incthod 1s radidtlon damagc. usmy

L'V. X-ra) or y-rays. This tc.cluuque is employed ~n purr host lattice or a

doped Iioat I I I ~ I I C ~ t { t ) ~ r \ c r . p : i r ~ ~ n , ~ g n ~ t ~ c center5 of this tkpe produced hq

this technique are not included in the present thesis. Hence, no further

discussion is given.

Instrumentation

The details oi'instrumentat~on and measurement techniques have been

I I I \ C L I \ S C L J C Z I C I I M Y C I ) 111 I I ~ C I J I U I . C [ I - ? ] . The s~hcmi l t~c d ~ t i g u n of an EPR

spcctron~erer 1s shown In Figure 2.1. From the resonance condition hu = gpB,

it fo i low~ that the EPR spectra can be measured by fixed frequency and

vanahlc tield or tixed field and variable tiequency; rt is always convenient to

folloi$ thc former procedure. Depending upon the Irradiation frequency, EPR

spectrometers are classified .I, S. S. K and Q band spectrometers, the most

comn~on ones are X and Q band spectrometers. At X-band, the frequency is

nonnally around 9 GHz. uith Cree-rltctron resonance field ar -320 mT, while

at Q-hand, the corresponding iaiuc> arc 35 GHz and I250 mT. The

approximate tiequency rdngcs and navelength of different bands are gi\en

helo\\ :

Bands S X K Q

Approxiniatc Frcquen~.y (Gt i / l 3 9 24 35

.Approximate Wa\ eietlgth (nm I YO 70 12 Y

Approx~~narc I:lcid (11iT) lilr g = 2 I I0 320 850 1250

Derailed descnpr~on ot' has~c pnnciplcs ~ n \ o i \ e d in EPR

Instrurnenrarion 1s given by Ingnm I ] a d Poole [:I. In order to o b s e n r 3

well resolved EPK spectruni, the Instrument baa to be operated under optlmum

Figure 2.1: Block dle&~drn ot'a t yp~s ;~ l X-band EPR spectrometer.

conditions of microwave power, mt~dulation amplitude, spectrometer gain,

filter time constant, scan range and scan time. The work described in this

thesis has been canied out on JEOL JES-TEl00 ESR spectrometer operating

at X-band frequencies, having a 100 kHz field modulation to obtain a first

denvative EPR spectrum. DPPH, with a g value of 2.0036, has been used for

g-factor calculattons

Crystal growth

Thc hll tnformdtiun ot a complex can be obtained from the EPR

meaaurements of single crystal rather than a powder or solution

measurements. Due to this reason, one prefers single crystals rather than

powdcrs and solutions. Hence, a hnef dtscusston about crystal grouPth is

mentioned The main technique inlolted tn crystal g o u z h is slou

einporatlon method. Crystals are gcnerall) g o w n by allowing a saturated

holutlon o f 3 matendl to lose sollent h \ rvsporation [5.6]. Many interesting

cr)stals can be gmun wtth little knouledge of fine details s~mply by

cbaporation oi'the sol\enr or temperature shmge. The evaporation of solvents

makes the solution aupers~rurated so that, 11 attempts to achieve the

'quilibrium saturated btate h) rejcctlng the seed crystals to solut~on.

However, care must be taken to prevent the solution becoming too much

supersaturated, becauar crystals would then appear spontaneously throughout

solut~on. The facton 11131 ~ontr01 [he growth process are:

I . character o f the solut~on

2, effect of additives and

3. operating variable such as [he degree of supersaturation and the

temperature range.

The choice of solvent is an Important factor that determines the growth

of a crystal from solution Grou.th o i a large crystal is almost impossible

unless B s ~ l \ e n t is found in i r h ~ c h thc scllute is substantially soluble In the

present work. warer ia used aa the >ol\ent fbr all the crystal growth. No

addit i~es arc added to the solution except the dopant. The rate of growth

dcpcnds on [he temperature at which the solution IS maintained. At higher

tempcratures, the groszh rare will he generally high. All the crystals are

g o w n at room tempcratures (I98 z 2 K).

Interpretation of EPR spectra

As one can rnraburc E P R \pcctra irom solution, powder and single

cr)rtsl sample>. the pr(ii.t.durt, to t~htain $pin-Harniltonian paramerers from

theses spectra murt he ~( i rn t~ t ied . .A hrief drscussion IS mentroned belo\\ In

order ti) calculate the g and A \dues . the fullov,ing expression has been used:

s - (SDI'I'II BOI'Y~I) R -----[:.I]

where B is the niapetic field p~sit ion at the EPR peak. B ~ p p ~ IS the field

Position carresp~nding to DPPH and g ~ p p ~ is the g-ialue of DPPH which is

equal to 2.0036. 'The g-\'slue IS dlrectly calculated uslng the spectrometer

tiequcncy at which resorlrln~c L I C ~ U ~ S . The expression IS as follows

g = (hu i PB) -----[?.?I

In this case, v is the resonance frequency.

The hyperfine (hf) coupling constant 'A ' is given by the field

separation between the hyperfine components. If the spacing is unequal, an

average of them IS taken as the value of .4. For n number of hypefine lines,

the average hyperfine valuc is given by

A f B , , - B , ) , ( n - l ) -----[2.3]

Here. B, is the field posltlon for the nth hyperfine line and BI is the first

hyperfine l~nc field posltlon.

Spcctrcl are mcasured both in hingle crystal and poly-crystalline forms.

A bnef outline of the interpretation is given below.

Powder and glasses

In powders ~ n d glas$es, the observed spectmm is a result of

juperposlrlon o i all pasa~ble onentntlons of single crystals giving rise to

stat~a[lcdly ue~ghted average. The ri~eor) o f powder l ~ n e shapes on EPR ha>

been given In drta~l b) beubuhl ['I. Sands [S] and Ibers and Swalen [ 9 ] . A

hnef p~ctonal sununary ofrlle evaiuat~on of pnnc~pal magnetic tensors such ar

g and A, for a Sew rcprt.sentstl\c cxalnples is given in Figure 2 . 2 . In most of

the cases, the princ~pal \slues are c~lculatrd from powder data. However

powder line shapes become compl~cated when more than one type of species

1s present and or when hyperfine i~ncs o\erlap, and especlaliy so when the

tensors do not c o ~ n c ~ d r . Thc first two c~)mpl~cations can be c~rcumvented to

home extend by lneasunny [he spcctrd at !\LO d~ffrrent riequencies, say S and

g11= g,,= gl

A1,=Az2 =h A,,= All g,, = g, = g,3 = g

*ll<A,2< A,,

/tS g,,>g,,>g33

I u3: 413

A, 1 = .& = A,,,

4 1 >&2< .4,, -

Figure 2.2: Schemal~c diagram imndic~tlng the calculat~on of principle values

o f ' m a p e t ~ c tensors tiom p~iwdrr data based on the delta funct~on line shape.

Q bands, then sorting out the field-dependent and field-independent terms in

the Hamiltonian. Sometimes, power saturation techniques [I, 21 and

temperature vanation will also help in this respect.

Single crystals

Many authora. for example, Schonland [ lo] , Weil and Anderson [I I],

l'ryce [ I ? ] . Geusic and Brown [ l j ] . Lund and Vanngard [I41 and Walier and

Koycrs [ IS ] have discussed In detail the procedure for the evaluation of the

principal values of magnetic tcnsors Aom single crystal measurements. The

method cunalsts of rneaauring the vanation of g'(0) for rotations about three

mutually perpendicular planes In rhc cystal, which may coincide with the

cr)stallo~raphic axt's or dre related ro the crystallographic axes by a simple

transtbrmatlon. From the maxima and minima obtained In the three

orthogonal planes, the matrix elements of the g' tensors can be der i~ed eas~ly

[ I O ] A Jacob! diagonailzation of thls matrix $vrs rise to the Eigen values

~orrcsponding to the principal ~a lueh of' the y tensor and the transfornation

Inarrlx. rrhich diogoi~~li,ea rhv eupen~nental g' rnatnx.. This matrix provides

thc direction coslnea of thebe tensors r r~ th respect to the three onhogonal

rolatlons. Hou,ever, compl~catiuns will anse, when more than one

~nagnetically distlnct siru pcr UINI cell is present, hecause no apnon

predictabihty of thc relation> bctrrccn sitea and spectra in the three planes.

This leads to se\eral pussible pemiutations leading to man) g: tensors. For

cxmplc , if a system hnb n sltes, then there are 3' tensors, including for not

performing a proper rotation, i.e., clockwise or anticlockwise. A careful

examination, howcver, invariably lends to the proper combinations and the

corresponding direction cosines. In the case of hyperfine tensor. when g is not

highly anisotrop~c, thc same procedure as above can be adopted. When this is

not the case, Schonland [lo] has suggested that it is necessary to follow the

variat~on of .g2A(9) in the three prins~pel planes. The reason for this is as

roll~)wh:

The Hamiltonian for a paranabmetic system, including only the

electronic Zeeman and hyperiine tern~s can be expressed as

H = p (gllBISi - g:2B2S2 A g?lB?Sj) + ( A I I S I I I AZ2S21> + A1jS313) -----[2.4]

Let (nl, n?, ni) be the direction cosines of the magnetic field B w ~ t h reference

to the axes ot rhc g tensor ~ n d hypertine tensor. Here, it is assumed that g and

hypefine tensors are coinc~dent. If M and m are the electron and nuclear spin

quantum numbers, then the energy le\els are given by:

EI,,, = gPBM t PKMm -----12.51

Herr g and K are glvcn by the equations

9 ,

g = (8, ;11~- + gr2'n:' t gJ'nl')l ' -----[2.6]

and

K = lig [ g l l ' ~ l 1 2 n l ' - y22'~22'n22 - g ~ 3 ' ~ ~ ~ 2 n 3 ' ] 1 ' -----12.71

The magnetic field Bm where the transition M , m>ttjM+l,m> occurs is gven

by

hu=gpB,-PK -----[2.8]

In other words,

If A 1s hyperfine sp l~ t t~ng and the I1ne5 are centered around (hulgp), then

A = W g ---42 101

In order to obtaln the matnx elements of the hqperfine tensor, the angular

tandtlon of ( g ~ ) ' IS cona~dered, alnie (gK) has a hnear angular dependence

on g Therefore

( g ~ ) ' = g " ~ ' ----[2 1 11

From t h ~ s equatlon the rnarrix elemcntj of the hyperfine tensor matnx are

rvdludted using the same pro~cdure ujed to get g tensor matnx

Schonland has Indicated the probable errors In the method descnbed

above to gel the pnnc~pal vdlueh of g and hy-perfine tensors But, the errors

u e vcry small compared w ~ t h the expenmental errors ~nvolved, such as

mountlng the c r \ d ah! : the sprc~tic axla, measurement of magnetlc field

Crystal -:ructurc of the host ldtt~ces

A br~e l ln~roduitlon of the iarloub host latt~ces employed In t h ~ s t h e m

is preacni~d here The d e t ~ i l irqa~di rtruitures are d~scussed In the respective

chapters S~ngle iryatai5 ot magneslum ammonlum phosphate htxahydrate

(MAPH), cadm~um potasslum phosphate hexahydrate (CPPH), cadrn~um

aod~um phosphate hexdhydrate (CSPH) and cobalt ammonlum phosphate

hcxdhydrdte (CoAl3H) drc. grown bv slow evaporation from the saturated

aqueous aolut~ons contalnlng magneslum sulphdte and mmonlum d~hydrogen

phosplldtc in cqulmolar quantitlea (tor MAPH), cadmlum sulphate and

potasslum dihydrogen phosphate (for CPPH), cadm~um sulphate and sodlum

d~hydrogen sulphate (for CSPH), cobalt sulphate and ammonium dlphosphate

(for CoAPH) wlth the corresponding paramagnettc impunty (about 1%)

All these types oi'cry\tals are ~ n a l o ~ u e s to the mineral (or b~omlneral)

sttuvlte vanety, M"M'P04 6H?O wltll M" = Mg, Cd, Co etc, M' = Na, K, TI,

I I I I I I ilc 1 1 i ~ j t 1 1 I I ~ ~ ~ X I I ~ . I I ~ L C O ~ t111\ ~lilncrill I.\ thdt I I I & ~cliltcd 1 0 11s

oecurtcncc In lluiil~n urlndry ~cdimcnta and vestcal and renal calcul~ 1171

Struvlte has a high degree of recurrancc and about 39% of stone suffering

p~ticlit\ cYI)crtcIIcc druvI1c ~ [ o I ~ c : , [I Y ] Struvlle 1s also formed In solls as a

reactlon product from phosphate tert~lizers [17]. It crystall~zes in the

onhorhomblc system, space group Pintt2, The unlr cell parameters are a =

0.6941(2) nm. b = 0 6137(!) nrn and c = 1 1199(2) nm The structure

conlairls lnabmesium ~ o n s surrounded by F I X oxygen atoms of water of

hydrdtlon The SIX Mg-0 bond d~statlce+ are O 7095, O 2103, 0.2071, 0.2042,

0.2071 and 2.042 nm

Slngle crystals o t cobalt sodlum sulphate hexahydrate (CoSSH) are

also obtained by the usual method of evaporation from cobalt sulphate and

aodlum sulphate Thls crystal belongs to the Tutton's salt vanety. CoSSH

belongs to monociln~c system wlth space group P(2lIa) [I91 There are two

~nolecules per unit cell ant1 the unlt cell dimenston valuer are. a = 0.9034 nm,

b = l.!184nm.c=06148nmdndU-l04.~'

Slngle crystals of hexa~mldazole cobalt sulphate (abbrev~ated as

HCoS) doped wlth Nl(I1) are g o w n according to a modlfied procedure g v e n

by Sandmark and Branden [20] The crystal structure of HCoS IS s~mllar to

that of HZDT (hexa~mldazole zlnc d~chlonde tetrahydrate) HZDT belongs to

the tnclln~c crystal class (space group p l ) with one formula unlt,

Zn(C,H4S2)6S04 4H20 per unlt cell w ~ t h the cell d~menslons a = 1 07, b =

0 94 dnd L = 0 84 nm, u = 120. (3 = 97 and y = 98' respectively

Single crysrals of h~(ll) /HCoN (Hexa~m~dazole cobalt nltrate) are

obtained by slow evaporation of an aqueous solutlon of lmldazole and cobalt

nitrdtc in the ratio ot 6 1, to whlch a small amount of n ~ c k e ~ nltrate IS added

Into the sy\tem, adjusting the pH to 6 9 wlth dl1 HNOJ NI(II)IHCON

crystallizes in the tngondl system w ~ t h R3 space group [21] The hexagonal

unlt cell has a = b = 1 2353 nm, c = I 4803 nrn The cobalt Ion 1s s~tuated at

the center of symmetry oi a tl~ghtly d~storted octahedron along the C; axls

such lhar all the Co-N bonds mdle utth t h ~ s an dngle of 56 3' Instead of

54 75" charactenst~c ot a regular octahedron

Direction cosines of the subshtutional sites

The alngle cryslal X-ray dnalys~s data prov~des the pos~tlonal

parameters p, q, r and the unlt ell dilnens~ons a, b, c and a, p, y For crystal

\ystem wlth non-orthogond crystal axes, the poslt~onal parameters p, q, r of

the VUIOUS atoms can be changed o \e r to an orthogonal framework and the

Cartesian co-ord~nates x, y, z could be calculated uslng the reiat~on

a b cos y L cos p ;;= [ O b sln y ( c i s iy ) (cos a - cos pcos y

I 0 0 d

where, d = [ c' - c' cos' I) - ( c2! sin'., ) (coi a - cos fl cos r )']I ' By setting the metdl atom a< [he ongin. the coordinates of the vanous

dtoma In the crystal surrounding the metal are calculated The normallzed

Caneq~an co-ord~ndtea of t h e x arorna glve the dlrectlon coslnes of the metal-

l~gdnd bond o! the co-ordinat~on pol:,hedron The direction cosines of these

maal- l~gand bonds can be compared with the d~rec t~on coslnes of the g and

.A- tensors, obtained by the procedure descnbed in the prevlous sectlon

S o ~ n u r ~ ~ n c \ . I[ 15 found tll,it tlic iildgnctlc tensor dlrect~ons colncldr with borne

o f th r bond directions, uhlch may not be so in low skmmetry cases

Spin-lattice relaxations

As d pararndbvnic Ion is incorporated Into a paramagnetic host, 11 w ~ l l

be Interestins to study the ndture and extent of dlpoidr lnteractlon As Co(l1)

l a EPR s~lcnr dt room tempernre, analyses ot EPR data at room temperature

has been done without much difficulty, because the EPR llnes are not

brodtlcned by the dlpoldr lnterdctlon Ilowever, as the temperature IS lowered,

d tremendous change in the line ~rilith haa been notlced, due to the dipolar-

dlpoldr interdctlon herueen the pdrdmJgnetlc host and the impunty Hence, d

pan~cular onentation 15 selected from the crystal onentation and the \anable

temperature measurements are made, from which the line widths (AB) are

~neahured It IS noticed tlii~r a\ the lcmperature 1s decreased, the line w~dth

~ncreahes with decrease In intcns~ty and below a certain temperature, the peaks

broadened almost to a straight 11ne Thc hame k ~ n d o f observat~on IS not~ced

even iiom the powder sample. T h ~ s type of line broadening IS mainly due to

the d~polar interaction of the host paramagnetlc lattice and the impurity. The

11nc-w~dth vanat~on of the paranagetic lmpunty hyperfine l ~ n e s In

para~iiag~lct~c Idltlcc car1 bc undcra~ood on the basis of host spin-lattice

relaxat~on mechanism The fast sp~n-lat t~ce relaxat~on of the host ions can

rilndolnly ~nloduldtc ihc d~polar lntcriitlon between the paramagnetlc host and

the ~nlpunty ~ o n a resulting In "Hosr spln-latt~ce relaxat~on narrowing" [22].

\Vlicli thc a p ~ ~ i - l ~ t t ~ c c reIa\dtion narrowing mechanism IS effect~ve, the host

>pin-lntt~cc relaxdt~on t ~ m e ( ' r ) IS glvcn by [22.23]

7.1 ; (3/7)(hl~gh[))(.l~,,, ~d ' , i ) -----[2.13]

~ d ' d = s . I ( ~ ~ P ~ ~ s ~ ( s ~ + I )

where,

gi, = the host g value

Sh =- the eftect~ve host spln and 11 IS taken to be li2

11 - the number ot hosr spins per u n ~ t ~ o l u m e whlch can be calculated

from the C ~ ~ ~ I ~ I I O ~ T J ~ ~ I C ddtn of the crystal lattlce and

AH,,,,, = the lmpunty l ~ n e wdth

The calculated sp~n-latt~ce relaxallon t~mes T I are plotted agalnst

temperature and the graph lndl~dtes that ds the temperature decreases the sptn-

latt~ce relaxahon t ~ m e T I Increases

SimFonia powder simulation

The s~mulat~on of the powder spectrum IS generally carned out to

venf) the expenmental spectrum with the theoret~cal one, obtalned by uslng

the 9pln Hamlltonlan parameters cdliuldted from the expenmental spectrum

The \iniulat~on of the pouder spectrum IS done uslng the computer program

51mi onla developed and suppiled bq Bmclier Lompany Thc algorithm used

In thc SimFon~d progrdm tor poirdcr s~nluldtlon 1s based on perturbatton

thvoi) i r l i ~ ~ l l 1s dn appro\lriiJrlon l're\~c~u,lq, perturbation theory has been

used In rhe Interpretailon of EPR spectra because of the speed of calculat~on

and the lntultlveness of the results i t 1s an approximate techn~que for findmg

the energy elgen value\ and elgen m t o r s of the spm-Hamiltonlan The

dssumptlon made 15 that there la a dolnindnt tnteractlon, whlch IS much larger

thdn the other Interdctlon\ As the domlnant ~nteractlon becomes larger when

comp~red to the ot'ler lnteractlon\, the approximallon becomes better The

five Interactions that are ~onsiderrd In the S~mFon~a s~mulat~on program for

!he powder sample xe

I Elu~tron~c Zecmdn lntcrdctloii I t IS the lnteractlon of the magnetlc

moment ot thc electron uith txterndlly appl~ed magnet~c field I e , the

nldbmetli tield from the spectrometer mdgnet

2 Zero-field splm~ng It occurs to electron~c systems m which the spin is

greater than 112

3 Nuclear hyperfine lnteractlon It IS an lnteractlon between the

tnagnetlc moment of the electron wlth the magnetic moment of the

nucleus

4 Nuclear Quadrupole ~nteraction It IS the lnteractlon between the

Quadmpole momcnt ot the nucleus w~ th the local electnc field

grddlents In the complex (for 5ystem havrng nuclear spln greater than

I 1)

5 huclear Zeeman Intcrdctlon I t is the lnteractlon uf the magnetlc

rnonlenl oi'the nuclcua wlth thc externally appl~ed magnetlc field.

The assumption made In the simulat~ons is that the electronic Zeeman

lnterdLllon 1s the lugest, tollowed by the zero-field spllnlng, hypertine

lnterdctlon, nuclear quadrupole lnteractlon dnd the nuclear Zeeman term is the

smdllest Penurbatlon theory works best when the ratlo between the

successlw ~nteractlons 1s at least ten If the 11mits exceeded, perturbat~on

theor) st111 gves a good plcrure of EPR spectrum, however, 11 may not be

su~table for the quantctatlve analys~a And lf the EPR spectrum 1s to be

slrnuldred wlth larger hypertine interactions, then second order perturbat~on

theory 1s selected to lncrease the accuracy of the s~mulatlon The zero-field

splitrlng 1s always treated to second order because they do not produce a non-

zero first order term

Only allowed EPR transltlons are simulated, but under some

clrcurnstances forbidden transltlona Lan also appear These corresponds to

s~multdneous f l ~ p of the nucleus and flop of the electron and forbidden EPR

llnes occur between the allowed trans~t~ons or a AMs = i 2 electronic

trans~t~ons These forb~dden l~nes are not simulated because perturbation

theorq 17 not the opt~mal method for calculating the~r posltlons and intensity

Thc S~niFon~d powdcr s~rnul~tlon progaln simulates EPR spectra for spin l i 2

to \pin 7'2 electronic systems For spln greater than 1'2, the zero-field

~ p l ~ t t l n g terms (D and E) arc implemented There are essent~ally no

restnitlons on the spln of the nucle~ All the naturally occumng spins have

been prugrdmmed The pnnclpal axes of the electronic Zeeman Interactton

and thc /era-tield splitting arc mumed to be colncldent

SlrnFon~d can a~mulate both types of line shapes I e , Lorentzlan and

Gaussldn, as well as combinat~on of the t a o Thls t e c h q u e 1s most effic~ent

for rnmy Ilne-cornpl~cated spectra Dcta~led theory of the powder spectra

s ~ m u l , ~ t ~ o n cdn he obtatned trom the rcferences [24, 251

Cornputcr Program EPR-3MR 1261

The program sets up rpln-Hamlltonlan (SH) mamces and determines

the~r c~gcn values (energlcs) uslng "cxact" d~agonal~zatton It IS a versatile

progrdm, having many operating models tailored to a var'ety of appllcat~ons.

Theses modes can he grouped Into four categones, In lncreaslng order of

complrx~ty as follows

I Energy-level calculation,

2 Spectrum slmulat~on

3 Companson wlth observed data,

4 Parameter optlmlzatlon

For each category, most of the operations of the lower categories

rernaln available, so that a good \\ay to learn how to use the program

etfo~ll \cly 1s lo aldrt dt tile lowe\t id t~gory dnd work one's way up

Categog' 1: In thls category, the user provldes the program w ~ t h SH

parameter$, dnd dlrectton and mayn~tudes of applled magnetlc fields

Curegory 2: In cdtegory 2 , the user dlao apeclfies an expenrn-nt, chosen from

tlcld-r~vcpl or Irequen~y-wept eleilron pararnabmetlc resonance (EPR) or

I I U L I L ~ I mdgnetli rerondnLc ( N M R ) , electron nucleus double resonance

(ELUOR) or electron spln e ~ h o envtlope modulat~on (ESEEM) In addltlon,

the user must ldrnrlty the trdnutlon\ ot Interest The "spectra" simulated

ionalsts ot srta oftranaitlon trequenclcs or mapet lc field values, dnd posslbly

r e l ~ t l \ r trdns~tlon probabil~tlca The program can dlso convolute these data

\r 1111 ,I I I I I L - ~ ~ I ~ ~ L lunit~on ( L o ~ L ~ ~ ~ I ' I ~ I dnd Gduaalan) to produce d plot

Catc'fiory 3: For thls Laregor) tht user also aupplles appropnate observed

\ ~ n g l r crystal data, w ~ t h trans~tloll labcla ~ s ~ l g n e d , and the probTam de tem~ne ,

the d e g e e of consistency 1~1th data c~iculated iiorn the @Yen SF parameters

This i J n ~ncludc an error dndlyala on ,I uacr-selected subqets of SH parameters

md!or mdbnerlc-field dlre~tlona

Category 4: In the category 4, the user-selected subsets of parameters may be

opt~mlzed, so as to g ~ v e better ageernent between observed and calculated

transltton trcquenctes These user5 a non-l~near least squares routlne, whlch

systemdt~cally vanes the punmeters so as to mlnlrnlze welghted difference

bctuccn obacwcd ~ n d cdlculated rrdnsltlon trequenc~es (or fields) In thts

cdtcgory, user-suppl~ed SH pdrdmctcrs need only be estimates or outnght

guc"~$ I l l l a progrdm lid\ bccn u,ctl In [he calculat~on of SH parameters for

,111 tlic ~ ~ \ I C I I I \ s ~ u d ~ c d tn 1h15 tlies~s

References

1. D. J . E. Ingram (ed.), "Biological and Biochemical Applications of

Electron Spin Resonance", Adan] Hilder LTD, London, (1969).

2. C. P. Poole, "Electron spill resonance", Second edition, Dover

Publ~cations, USA, ( 1996).

3. R. S. Alger. "Electron Pa!.amagnetic Resonance Technique and

Applications." Interscicnce, New York, (1968).

4. T. H. Wiirnshurst. "Electron Spin Resonance Spectrometer", Plenum,

Neir York, (I OhX).

5. J . J . Gilman, "Thc art and Sc~cnce ofGrowing crystals", John Wiley &

Son Inc., New York. (1963).

6. J. C, Bncc, "Tlie growth ot crystals from liquids", North-Holland

Publishing Company, London. (1973).

7. E. K. Kneubuhi, J . Chztn. Phys., 33 (1960) 1074.

8. R . H. Sands. Phys. Rev., 99 ( 1 9 5 5 ) 1222.

9. J . A. Ibers, J. D. Siralen, Phys. Re\ . , 127 (1962) 1914.

lo. D. S. Schonland, I'roc. I'll), Soc.. 73 (1959) 788.

l 1 . J . A. Weil, H. A. Andersun, J . Chem. Phys., 28 (1958) 864.

12. 11. H. L. Prycc, Proc. I'i~ys. Soc., A63 (1950) 25.

13. J . E. Gcusic, L. C Brown, Ph!s. Rcv., 112 (1958) 64.

14. A . Lund. T. Vanngard. J . Chem. Phys., 42 (1965) 2919.

15. W. G. Waller, Max T. Rogers, J . M a p . Res., 9 (1973) 92.

16. M. L. Mathew, W. Schroeder. Acta Cryst., B35 (1979) 11.

17. F. Abbona, R. Bo~stelle, J. C'ryst. Growth., 46 (1979) 339; and refs

therein.

18. E. Takasaki, Urol. Intern., 30 (1975) 228.

19. J . Whitnail. C. H . L. Kennard, K. K. Nimmo, F. H. Moore, Cryst.

Struct. Commun., 4 (1 975) 7 17.

20. C, Sandmark, C. I. Branden, .4cla. Chcm. Scand., 21 (1967) 993.

21. A. Santoro, A. D. Michell, M. Zocchi, C. W. Reimann, Acta Cryst.,

8 2 5 ( 1969) 842.

2 2 . 7'. M~tsuma, J . Phys. Soc. Jpn.. 17 (1962) 128.

73. 5, K. Mlhtira, M i ~ g l ~ . ~ { C ~ O I I . I<cv.. 12 (1987) 191.

24. A. Abragam, B. Bleaney, "Electron Paramagnetic Resonance of

Traniitlon metal Ions". Clarendon Press, Oxford, (1970).

25. J . R. I'ilbrou, "Transition Ion Electron Paramagnetic Resonance",

Clarcndon Press. Osfurd. (1990).

26. EPR-N.MR Progam dcveloprd by F. Clark, R. S. Dickson, D. B.

Fulton, J . Isoya. A. Lent. D, G . LIcGavin, M. J . Mombourquette, R. H.

D, Suttall, 1'. S. Rao. H . Rinncber~, W. C. Tennant, J. A. Weil,

Cniversity cf'Saskatcheivan. Saskatoon, Canada (1996).